Combining Texts

All the ideas for 'Logicism Revisited', 'Remarks on the Foundations of Mathematics' and 'talk'

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11 ideas

3. Truth / H. Deflationary Truth / 1. Redundant Truth
'It is true that this follows' means simply: this follows [Wittgenstein]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Two and one making three has the necessity of logical inference [Wittgenstein]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism is a bulwark of logical positivism [Musgrave]
Formalism seems to exclude all creative, growing mathematics [Musgrave]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / a. Consciousness
If the present does not exist, then consciousness must be memory of the immediate past [Marshall]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]